Serpentine pendulum

1. Content:

Exhibition items consist of a booth, crossbeams, small balls, and thin wire combinations. A row of small balls are hung on the crossbeam with thin wires, and each ball has a different cycloid length, so the swing period of each pendulum is also different, thus forming a serpentine pendulum. When the ball pendulum starts swinging, initially due to the small and regular difference in angle, the entire pendulum looks like a dancing snake. After swinging multiple times, the differences gradually increase, and the ball seems to swing in a disorderly manner. After continuing to swing, the swing state will change again, sometimes forming a row of neat light columns that swing relative to each other, and sometimes interlocking like long snakes... As the number of swings increases, a row of neat small balls become dynamic snake like swings.

2. Principle:

In this operation, the length of the serpentine pendulum decreases in a regular pattern, so the periods of all pendulums also decrease in a regular pattern. In terms of the size of the swing angle, the swing angle also decreases in a regular pattern. Therefore, after starting to swing, initially due to the small difference in angle and the regular difference, it looks like a fluctuating snake like swing. After multiple swings, the differences gradually increased and appeared to be chaotic. After continuing to swing, until the angles of odd and even single swings reach integer multiples and half multiples, respectively, the situation of splitting into two sides can be observed.

3. Purpose:

This exhibition items showcase a small ball that can be freely swung by hanging a suspension line on a beam. Ignoring air resistance, its period is only related to the acceleration of gravity and the length of the cycloid.